US 20090207414 A1 Abstract An apparatus is provided for measuring a frequency-domain optical coherence tomography power spectrum from a sample. The apparatus includes a broadband light source, an optical spectrum analyzer, and a partially reflective element optically coupled to the light source, to the optical spectrum analyzer, and to the sample. A first portion of light from the light source is reflected by the partially reflective element and propagates to the optical spectrum analyzer. A second portion of light from the light source propagating through the partially reflective element, impinging the sample, reflecting from the sample, and propagating to the optical spectrum analyzer.
Claims(12) 1. An apparatus for measuring a frequency-domain optical coherence tomography power spectrum from a sample, the apparatus comprising:
a broadband light source; an optical spectrum analyzer; and a partially reflective element optically coupled to the light source, to the optical spectrum analyzer, and to the sample, wherein a first portion of light from the light source is reflected by the partially reflective element and propagates to the optical spectrum analyzer, a second portion of light from the light source propagating through the partially reflective element, impinging the sample, reflecting from the sample, and propagating to the optical spectrum analyzer. 2. The apparatus of 3. The apparatus of 4. The apparatus of 5. The apparatus of 6. The apparatus of 7. The apparatus of 8. The apparatus of 9. The apparatus of 10. The apparatus of 11. The apparatus of means for obtaining a magnitude spectrum of a complex spatial Fourier transform of a complex intermediate function, the complex intermediate function dependent on the complex scattering function of a portion of a sample under analysis, the magnitude spectrum obtained from power spectrum data of frequency-domain optical coherence tomography of the portion of the sample under analysis; means for estimating an estimated phase term of the complex spatial Fourier transform; means for multiplying the magnitude spectrum and the estimated phase term together to generate an estimated complex spatial Fourier transform; means for calculating an inverse Fourier transform of the estimated complex spatial Fourier transform, wherein the inverse Fourier transform of the estimated complex spatial Fourier transform is a spatial function; and means for calculating an estimated intermediate function by applying at least one constraint to the inverse Fourier transform of the estimated complex spatial Fourier transform. 12. The apparatus of (a) providing a magnitude spectrum of a complex spatial Fourier transform of a complex intermediate function, the complex intermediate function dependent on the complex scattering function of the portion of the sample under analysis, the magnitude spectrum obtained from power spectrum data of frequency-domain optical coherence tomography of the portion of the sample under analysis; (b) providing an estimated phase term of the complex spatial Fourier transform; (c) multiplying the magnitude spectrum and the estimated phase term together to generate an estimated complex spatial Fourier transform; (d) calculating an inverse Fourier transform of the estimated complex spatial Fourier transform, wherein the inverse Fourier transform of the estimated complex spatial Fourier transform is a spatial function; and (e) calculating an estimated intermediate function by applying at least one constraint to the inverse Fourier transform of the estimated complex spatial Fourier transform. Description This application is a divisional of U.S. patent application Ser. No. 11/384,170, filed Mar. 17, 2006, and incorporated in its entirety by reference herein, and which claims the benefit of U.S. Provisional Application No. 60/662,652, filed Mar. 17, 2005, which is incorporated in its entirety by reference herein. 1. Field of the Invention The present invention relates generally to apparatuses and methods for optical coherence tomography, and more specifically to apparatuses and methods for providing improved optical coherence tomography images. 2. Description of the Related Art Optical coherence tomography (OCT) is widely used in medicine to image tissues of various part of the body. See, e.g., T. Asakura, “ In certain embodiments, a method determines the complex scattering function of a portion of a sample under analysis. The method comprises providing a magnitude spectrum of a complex spatial Fourier transform of a complex intermediate function. The complex intermediate function is dependent on the complex scattering function of the portion of the sample under analysis. The magnitude spectrum is obtained from power spectrum data of frequency-domain optical coherence tomography of the portion of the sample under analysis. The method further comprises providing an estimated phase term of the complex spatial Fourier transform. The method further comprises multiplying the magnitude spectrum and the estimated phase term together to generate an estimated complex spatial Fourier transform. The method further comprises calculating an inverse Fourier transform of the estimated complex spatial Fourier transform. The inverse Fourier transform of the estimated complex spatial Fourier transform is a spatial function. The method further comprises calculating an estimated intermediate function by applying at least one constraint to the inverse. Fourier transform of the estimated complex spatial Fourier transform. In certain embodiments, a computer system comprises means for obtaining a magnitude spectrum of a complex spatial Fourier transform of a complex intermediate function. The complex intermediate function is dependent on the complex scattering function of a portion of a sample under analysis. The magnitude spectrum is obtained from power spectrum data of frequency-domain optical coherence tomography of the portion of the sample under analysis. The computer system further comprises means for estimating an estimated phase term of the complex spatial Fourier transform. The computer system further comprises means for multiplying the magnitude spectrum and the estimated phase term together to generate an estimated complex spatial Fourier transform. The computer system further comprises means for calculating an inverse Fourier transform of the estimated complex spatial Fourier transform. The inverse Fourier transform of the estimated complex spatial Fourier transform is a spatial function. The computer system further comprises means for calculating an estimated intermediate function by applying at least one constraint to the inverse Fourier transform of the estimated complex spatial Fourier transform. In certain embodiments, an apparatus measures a frequency-domain optical coherence tomography power spectrum from a sample. The apparatus comprises a broadband light source. The apparatus further comprises an optical spectrum analyzer. The apparatus further comprises a partially reflective element optically coupled to the light source, to the optical spectrum analyzer, and to the sample. A first portion of light from the light source is reflected by the partially reflective element and propagates to the optical spectrum analyzer. A second portion of light from the light source propagates through the partially reflective element, impinges the sample, reflects from the sample, and propagates to the optical spectrum analyzer. In certain embodiments described herein, the concept of minimum-phase functions is applied to improve optical coherence tomography systems. Certain embodiments described herein advantageously provide a simple processing technique for the conventional frequency-domain OCT configuration that enables a better signal-to-noise ratio, an improved measurement range, and that requires a lower-resolution optical spectrum analyzer than the currently existing processing techniques. Certain embodiments described herein rely on the property of minimum-phase functions (MPFs) to advantageously allow a function, complex or real, to be recovered from only its Fourier transform (FT) magnitude data. Certain embodiments described herein are useful in computer-implemented analyses of the complex field scattering function of frequency-domain OCT. The general-purpose computers used for such analyses can take a wide variety of forms, including network servers, workstations, personal computers, mainframe computers and the like. The code which configures the computer to perform such analyses is typically provided to the user on a computer-readable medium, such as a CD-ROM. The code may also be downloaded by a user from a network server which is part of a local-area network (LAN) or a wide-area network (WAN), such as the Internet. The general-purpose computer running the software will typically include one or more input devices, such as a mouse, trackball, touchpad, and/or keyboard, a display, and computer-readable memory media, such as random-access memory (RAM) integrated circuits and a hard-disk drive. It will be appreciated that one or more portions, or all of the code may be remote from the user and, for example, resident on a network resource, such as a LAN server, Internet server, network storage device, etc. In typical embodiments, the software receives as an input a variety of information concerning the material (e.g., structural information, dimensions, previously-measured magnitudes of reflection or transmission spectra). In typical OCT configurations, such as those shown in In the frequency-domain OCT configuration schematically illustrated by
where g(z′)=R·δ(z′)+ƒ(z′−z where G(ƒ) is the spatial FT of g(z′)=R·δ(z′)+ƒ(z′−z The conventional processing techniques of frequency-domain OCT measurements are based on a processing algorithm which directly takes the inverse FT of Eq. (2). Certain embodiments described herein are compared to the conventional processing techniques by assuming that S(ƒ) is broad enough to present a simple and fair comparison by assuming that, without loss of generality, the constant s has been dropped, i.e., I(ƒ)≈|G(ƒ)| In the conventional processing techniques, taking the inverse Fourier transform (IFT) of the measured OSA spectrum (I(ƒ)≅|G(ƒ)| where A.C. denotes the complex auto-correlation function, and ‘*’ denotes the complex conjugate operation. The important term for the recovery of the tissue scattering function is the last term of Eq. (3), i.e., R*ƒ(z−z Certain embodiments described herein utilize a simple processing technique that is based on minimum-phase functions (MPFs) to improve the resolution, the signal-to-noise ratio, and the measurement range of the recovered images in frequency-domain OCT systems. The intermediate function g(z′)=R·δ(z′)+ƒ(z′−z For the intermediate function g(z′)=R·δ(z′)+ƒ(z′−z It is generally not possible to fully recover a one-dimensional function from the knowledge of its FT magnitude alone. However, there are families of functions which are exceptions to this rule for which the FT phase can be recovered from the FT magnitude alone, and visa versa. One exemplary such family is the family of minimum-phase functions (MPFs). An MPF is characterized by having a z-transform with all its poles and zeros either on or inside the unit circle. As a result of this property, the FT phase and the logarithm of the FT magnitude of an MPF are Hilbert transforms of one another. See, e.g., V. Oppenheim and R. W. Schafer, “ In certain embodiments, this recovery of the function of interest (e.g., the intermediate function g(z′)=R·δ(z′)+ƒ(z′−z A second approach for the recovery of the function of interest (e.g., the intermediate function g(z′)=R·δ(z′)+ƒ(z′−z In certain embodiments, the only quantity that is fed into the method Since the FT phase term is missing from the measurement, an initial guess for the phase, φ In certain embodiments, the magnitude spectrum and the estimated phase term are multiplied together to generate an estimated complex spatial Fourier transform |G In certain embodiments in which the intermediate function g(z) has a known spatial extent (e.g., to be less than 1 millimeter deep), the operational block In certain embodiments, the FT of the estimated intermediate function g In certain other embodiments, the loop is repeated a predetermined number of times (e.g., 100). In certain embodiments, the predetermined number of times is selected to be sufficiently large so that the method achieves, or is close to achieving, convergence. In certain embodiments, at the end of the n-th iteration, g Empirical results indicate that such iterative error-reduction methods converge to the minimum-phase function corresponding to a given FT magnitude. (See, e.g., T. F. Quatieri, Jr., and A. V. Oppenheim, “ To understand intuitively which physical functions such as g(z′) are likely to be minimum-phase functions, g
for m samples of the function, satisfies the following inequality:
for all possible values of m>0. In Eq. (4), g(n) represents any of the functions that have the same FT magnitude as g Recovering ƒ(z) from only the knowledge of |G(ƒ)| using error-reduction methods compatible with certain embodiments described herein advantageously provides significant advantages in frequency-domain OCT over the conventional processing approaches. In certain embodiments, the error-reduction method does not utilize a minimum constraint for z In an example numerical simulation, to simulate a rather challenging problem, the complex tissue scattering function is simulated to be a uniform random variable, both in magnitude and phase, as shown by solid lines in The solid lines of The parameter of the ratio of R to max {|ƒ(z′)|} indicates how close the effective complex scattering function g(z′)=R·δ(z′)+ƒ(z′−z In certain embodiments, the reference mirror used in the lower arm of the Michelson interferometer shown in For certain embodiments in which an angled fiber end Various embodiments of the present invention have been described above. Although this invention has been described with reference to these specific embodiments, the descriptions are intended to be illustrative of the invention and are not intended to be limiting. Various modifications and applications may occur to those skilled in the art without departing from the true spirit and scope of the invention as defined in the appended claims. Referenced by
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